LMFDB - Family of higher genus curves with automorphisms search results

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Genus	Dimension of the family	Group order	Hyperelliptic curves	Full automorphism group

Quotient genus	Signature	Group identifier	Cyclic trigonal curves

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Results (1-50 of 164 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
5.20-2.0.2-20-20.4	$5$	$0$	$C_{20}$	$20$	$0$	$[ 0; 2, 20, 20 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
5.20-2.0.2-20-20.2	$5$	$0$	$C_{20}$	$20$	$0$	$[ 0; 2, 20, 20 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
5.20-2.0.2-20-20.3	$5$	$0$	$C_{20}$	$20$	$0$	$[ 0; 2, 20, 20 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
5.20-2.0.2-20-20.1	$5$	$0$	$C_{20}$	$20$	$0$	$[ 0; 2, 20, 20 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
6.20-2.0.4-5-20.1	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
6.20-2.0.4-5-20.5	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
6.20-2.0.4-5-20.4	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
6.20-2.0.4-5-20.3	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
6.20-2.0.4-5-20.2	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
6.20-2.0.4-5-20.8	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
6.20-2.0.4-5-20.7	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
6.20-2.0.4-5-20.6	$6$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 5, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
7.20-2.0.4-10-20.1	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
7.20-2.0.4-10-20.8	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
7.20-2.0.4-10-20.4	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
7.20-2.0.4-10-20.3	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
7.20-2.0.4-10-20.5	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
7.20-2.0.4-10-20.6	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
7.20-2.0.4-10-20.7	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
7.20-2.0.4-10-20.2	$7$	$0$	$C_{20}$	$20$	$0$	$[ 0; 4, 10, 20 ]$	$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
8.20-2.0.5-20-20.5	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,5,9,3,7)(2,6,10,4,8)(11,15,19,13,17)(12,16,20,14,18),\ldots$
8.20-2.0.5-20-20.2	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,3,5,7,9)(2,4,6,8,10)(11,13,15,17,19)(12,14,16,18,20),\ldots$
8.20-2.0.5-20-20.7	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,7,3,9,5)(2,8,4,10,6)(11,17,13,19,15)(12,18,14,20,16),\ldots$
8.20-2.0.5-20-20.1	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,3,5,7,9)(2,4,6,8,10)(11,13,15,17,19)(12,14,16,18,20),\ldots$
8.20-2.0.5-20-20.3	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,3,5,7,9)(2,4,6,8,10)(11,13,15,17,19)(12,14,16,18,20),\ldots$
8.20-2.0.5-20-20.4	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,5,9,3,7)(2,6,10,4,8)(11,15,19,13,17)(12,16,20,14,18),\ldots$
8.20-2.0.5-20-20.6	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,5,9,3,7)(2,6,10,4,8)(11,15,19,13,17)(12,16,20,14,18),\ldots$
8.20-2.0.5-20-20.8	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,7,3,9,5)(2,8,4,10,6)(11,17,13,19,15)(12,18,14,20,16),\ldots$
8.20-2.0.5-20-20.9	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,7,3,9,5)(2,8,4,10,6)(11,17,13,19,15)(12,18,14,20,16),\ldots$
8.20-2.0.5-20-20.11	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14),\ldots$
8.20-2.0.5-20-20.12	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14),\ldots$
8.20-2.0.5-20-20.10	$8$	$0$	$C_{20}$	$20$	$0$	$[ 0; 5, 20, 20 ]$	$(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14),\ldots$
9.20-2.0.10-20-20.7	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,8,3,10,5,2,7,4,9,6)(11,18,13,20,15,12,17,14,19,16),\ldots$
9.20-2.0.10-20-20.6	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,8,3,10,5,2,7,4,9,6)(11,18,13,20,15,12,17,14,19,16),\ldots$
9.20-2.0.10-20-20.9	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,6,9,4,7,2,5,10,3,8)(11,16,19,14,17,12,15,20,13,18),\ldots$
9.20-2.0.10-20-20.12	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,6,9,4,7,2,5,10,3,8)(11,16,19,14,17,12,15,20,13,18),\ldots$
9.20-2.0.10-20-20.3	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,4,5,8,9,2,3,6,7,10)(11,14,15,18,19,12,13,16,17,20),\ldots$
9.20-2.0.10-20-20.14	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,10,7,6,3,2,9,8,5,4)(11,20,17,16,13,12,19,18,15,14),\ldots$
9.20-2.0.10-20-20.10	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,6,9,4,7,2,5,10,3,8)(11,16,19,14,17,12,15,20,13,18),\ldots$
9.20-2.0.10-20-20.15	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,10,7,6,3,2,9,8,5,4)(11,20,17,16,13,12,19,18,15,14),\ldots$
9.20-2.0.10-20-20.13	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,10,7,6,3,2,9,8,5,4)(11,20,17,16,13,12,19,18,15,14),\ldots$
9.20-2.0.10-20-20.1	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,4,5,8,9,2,3,6,7,10)(11,14,15,18,19,12,13,16,17,20),\ldots$
9.20-2.0.10-20-20.2	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,4,5,8,9,2,3,6,7,10)(11,14,15,18,19,12,13,16,17,20),\ldots$
9.20-2.0.10-20-20.4	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,4,5,8,9,2,3,6,7,10)(11,14,15,18,19,12,13,16,17,20),\ldots$
9.20-2.0.10-20-20.5	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,8,3,10,5,2,7,4,9,6)(11,18,13,20,15,12,17,14,19,16),\ldots$
9.20-2.0.10-20-20.8	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,8,3,10,5,2,7,4,9,6)(11,18,13,20,15,12,17,14,19,16),\ldots$
9.20-2.0.10-20-20.16	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,10,7,6,3,2,9,8,5,4)(11,20,17,16,13,12,19,18,15,14),\ldots$
9.20-2.0.10-20-20.11	$9$	$0$	$C_{20}$	$20$	$0$	$[ 0; 10, 20, 20 ]$	$(1,6,9,4,7,2,5,10,3,8)(11,16,19,14,17,12,15,20,13,18),\ldots$
10.20-2.0.2-2-20-20.2	$10$	$0$	$C_{20}$	$20$	$1$	$[ 0; 2, 2, 20, 20 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
10.20-2.0.2-2-20-20.3	$10$	$0$	$C_{20}$	$20$	$1$	$[ 0; 2, 2, 20, 20 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.